Constant-Time Addition and Simultaneous Format Conversion Based on Redundant Binary Representations
IEEE Transactions on Computers
Constant-time addition with hybrid-redundant numbers: Theory and implementations
Integration, the VLSI Journal
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Intermediate Signed Digit (SD) representation can facilitate fast and compact VLSI implementations of partial product accumulation trees. It achieves a reduction ratio of 2:1 at every level and also leads to more regular layouts. Its disadvantage is that the number of bit lines that need to routed can be high. This can lead to a significant area overhead especially at smaller feature sizes where the wire/interconnect area and delay can be dominant. A Hybrid Signed Digit (HSD) representation lets some of the digits be unsigned bits, thereby reducing the number of bit lines. By arbitrarily varying the positions of and distances between consecutive signed digits, this representation can trade off latency for area and offers a continuum of choices between the two's complement representation on the one hand and fully Signed Digit (FSD or simply SD) representation on the other.In this paper, we illustrate an A T (area 脳 delay) efficient multiplier based on the HSD-1 representation which is one of the many possible HSD formats, wherein every alternate digit is signed and the rest are unsigned (ordinary) bits. It is seen that multipliers based on HSD-1 format require more transistors than those based on FSD format. However, they require fewer bit lines to be routed, which substantially reduces the interconnect area; thereby leading to a reduction in the total VLSI area and a lower A T product. The design reaffirms that the interconnect area can be siginficant especially at small feature sizes.